There is no shortage of restaurants and cafes in Lucca. We really enjoyed Osteria San Giorgio eating their charming interior courtyard Via S. Giorgio, 26 if you want a specific recommendation.
I heard good things about Osteria Dal Manzo Via Cesare Battisti, 28 and it's right next door to a bike rental place - Ride the Walls - so maybe that's 'two birds' in terms of what you're looking to do.
In Italy osterias serve traditional local food in cooked in traditional ways if that's what you're looking for. Trattoria are casual but can be more modern in foods and styles and flair. If you want something simple, cheap and fast look for a Caffeteria which it technically a coffee place but usually has simple food. Bar Caffetteria La Colonna in Lucca was nice Piazza Santa Bianca, 2 but there's no reason to seek it out versus many of the others in town.
Enjoy Lucca,
=Tod